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<p>This study formulates and rigorously analyzes a novel viral infection model that integrates two critical biological mechanisms: full logistic proliferation of susceptible cells and cytokine-mediated infection enhancement. The basic reproduction number is defined as an epidemic threshold which serves as a critical determinant for infection clearance. Employing analytical techniques including M-matrix theory and Lyapunov function construction integrated with Barbalat’s lemma, we provide a complete characterization of global stability for both the infection-free and infection equilibrium. By regarding the proliferation rate as the bifurcation parameter, we conduct a comprehensive analysis of the existence and properties of the Hopf bifurcation. The dynamical behavior caused by the existence of logistic proliferation characteristics through Hopf bifurcation is much more complex than that of the model without this term. Moreover, our findings reveal that neglecting cytokine-enhancement mechanisms may lead to significant underestimation of infection potential, a conclusion further corroborated through sensitivity analysis of <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="12190_2025_2593_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="TEX">\(R_0\)</EquationSource> </InlineEquation>. Numerical simulations not only validate the theoretical results but also uncover an intriguing “endemic bubble” phenomenon. These results contribute to a deeper understanding of viral infection dynamics.</p>

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Dynamical analysis for a cytokine-enhanced viral infection model with logistic proliferation

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • Jinhu Xu,
  • Xueru Liu,
  • Suxia Zhang,
  • Aili Wang

摘要

This study formulates and rigorously analyzes a novel viral infection model that integrates two critical biological mechanisms: full logistic proliferation of susceptible cells and cytokine-mediated infection enhancement. The basic reproduction number is defined as an epidemic threshold which serves as a critical determinant for infection clearance. Employing analytical techniques including M-matrix theory and Lyapunov function construction integrated with Barbalat’s lemma, we provide a complete characterization of global stability for both the infection-free and infection equilibrium. By regarding the proliferation rate as the bifurcation parameter, we conduct a comprehensive analysis of the existence and properties of the Hopf bifurcation. The dynamical behavior caused by the existence of logistic proliferation characteristics through Hopf bifurcation is much more complex than that of the model without this term. Moreover, our findings reveal that neglecting cytokine-enhancement mechanisms may lead to significant underestimation of infection potential, a conclusion further corroborated through sensitivity analysis of \(R_0\) . Numerical simulations not only validate the theoretical results but also uncover an intriguing “endemic bubble” phenomenon. These results contribute to a deeper understanding of viral infection dynamics.